# How to 3D plot a volume of revolution?

Posted 10 years ago
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 HiI'm currently teaching how to calculate volumes of revolution using integration,for e.g. suppose f(x)=x^2 is rotated 360 degrees about the x-axis from x = 2 to x=4, the volume generated would be given byIntegral[Pi(f(x))^2,2,4]What I'm trying to do is plot the generated volume for explanation and demonstration purposes.some of the more complicated examples are something like, The region bounded by the curve y=9-x^2, x=2 and the x-axis is rotated 2Pi radians about the y-axis, calculate the volume of the solid generated.I know how to calculate the actual volume, but is there any easy way of plotting the solid formed in mathematica.
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Posted 10 years ago
 Dear Sean,I thought that RevolutionPlot3D only shows the surface, i.e.RevolutionPlot3D[Sqrt[t], {t, 0, 4}, AspectRatio -> 1] I thought that the question was how to plot a "solid", i.e the volume not the surface. I tried the option "Filling", but that does apparently not work. Is there an option to get RevolutionPlot3D to draw solids? BTW, there is this nice demonstration:http://demonstrations.wolfram.com/SolidsOfRevolution/but as far as I can see the author did not use RevolutionPlot3D either.
Posted 10 years ago
 RevolutionPlot3D is also very useful for plotting rotated functions in general if you want to show it done with less math.
Posted 10 years ago
 Dear Hifas,are you looking for something like this?RegionPlot3D[ Sqrt[y^2 + z^2] < x^2, {z, -16, 16}, {y, -16, 16}, {x, 2, 4}]which gives 